The seminar is joint for the division of Analysis and Probability and its main themes are Mathematical Physics, Probability Theory and Harmonic and Functional Analysis. The seminar is encouraged to be aimed at a broader audience, but some talks may be of a more specialised nature.
The talks in the seminar are usually 60 minutes, including questions.

At the moment, the seminar takes place via Zoom. See schedule below for links to Zoom meetings.

Should you have any questions or suggestions, feel free to email one of the organizers Jakob Björnberg (jakobbj 'at' chalmers.se, Probability Theory), Erik Broman (broman 'at' chalmers.se, Probability Theory) or Genkai Zhang (genkai 'at' chalmers.se, Analysis).

Should you have any questions or suggestions, feel free to email one of the organizers Jakob Björnberg (jakobbj 'at' chalmers.se, Probability Theory), Erik Broman (broman 'at' chalmers.se, Probability Theory) or Genkai Zhang (genkai 'at' chalmers.se, Analysis).

**Coming seminars****2021-10-19 at 13:15, Zoom**

Eveliina Peltola (Bonn and Aalto)

Eveliina Peltola (Bonn and Aalto)

*On Loewner evolutions with jumps*

I discuss the behavior of Loewner evolutions driven by a Levy process. Schramm's celebrated version (Schramm-Loewner evolution), driven by standard Brownian motion, has been a great success for describing critical interfaces in statistical physics. Loewner evolutions with other random drivers have been proposed, for instance, as candidates for finding extremal multifractal spectra, and some tree-like growth processes in statistical physics. Questions on how the Loewner trace behaves, e.g., whether it is generated by a (discontinuous) curve, whether it is locally connected, tree-like, or forest-like, have been partially answered in the symmetric alpha-stable case. We consider the case of general Levy drivers.

This talk is based on joint work with Anne Schreuder (Cambridge).

The seminar will be held via Zoom and broadcasted on a bigger screen in the seminar room MVL14. Members of the department will receive the link and password via mail, and can also attend in MVL14. Others interested are welcome to attend on Zoom and can get the link by contacting one of the organizers (please inform us who you are).

**2021-11-09 at 13:15, MVL14 and Zoom**

Clemens Weiske (Chalmers)

Clemens Weiske (Chalmers)

**2021-11-16 at 13:15, MVL14 and Zoom**

Hermann Thorisson (University of Iceland)

Hermann Thorisson (University of Iceland)

**2021-11-23 at 13:15, MVL14 and Zoom**

Edwin Wedin (Chalmers)

Edwin Wedin (Chalmers)

**2022-01-25 at 13:15, Zoom**

Sabine Jansen (Munich)

Sabine Jansen (Munich)

**Previous seminars**

**2021-06-08 at 13:15**

Nina Gantert (Munich)

Nina Gantert (Munich)

*The TASEP on trees*

We study the totally asymmetric simple exclusion process (TASEP) on trees where particles are generated at the root. Particles can only jump away from the root, and they jump from x to y at rate r_{x,y} provided y is empty. Starting from the all empty initial condition, we show that the distribution of the configuration at time t converges to an equilibrium. We study the current and give conditions on the transition rates such that the current is of linear order or such that there is zero current, i.e. the particles block each other. A key step, which is of independent interest, is to bound the first generation at which the particle trajectories of the first n particles decouple. Based on joint work with Nicos Georgiou and Dominik Schmid

**2021-06-15 at 13:15**

Augusto Teixera (IMPA, Brazil)

Augusto Teixera (IMPA, Brazil)

*Phase transition for percolation on randomly stretched lattices*

In this talk we study the existence/absence of phase transitions for Bernoulli percolation on a class of random planar graphs. More precisely, the graphs we consider have vertex sets given by Z^2 and we start by adding all horizontal edges connecting nearest neighbour vertices. This gives us a disconnected graph, composed of infinitely many copies of Z, with the trivial behavior p_c(Z) = 1. We now add to G vertical lines of edges in {X_i}xZ, where the points X_i are given by an i.i.d. integer-valued renewal process with inter arrivals distributed as T. This graph G now looks like a randomly stretched version of the nearest neighbour graph on Z^2. In this talk we show an interesting phenomenon relating the existence of phase transition for percolation on G with the moments of the variable T. Namely, if E(T^{1+eps}) is finite, then G almost surely features a non-trivial phase transition. While if E(T^{1-eps}) is infinite, then p_c(G) = 1.

This is a joint work with Hilário, Sá and Sanchis.

**2021-09-14 at 15:15 -- note the later time than usual**

Russell Lyons (Bloomington, Indiana)

Russell Lyons (Bloomington, Indiana)

*Monotonicity is special for continuous-time random walks on groups*

Consider continuous-time random walks on Cayley graphs where the rate assigned to each edge depends only on the corresponding generator. We show that the limiting speed is monotone increasing in the rates for infinite Cayley graphs that arise from Coxeter systems, but not for all Cayley graphs. On finite Cayley graphs, we show that the distance to stationarity is monotone decreasing in the rates for Coxeter systems and for abelian groups, but not for all Cayley graphs. We also find several examples of surprising behaviour in the dependence of the distance to stationarity on the rates. This is joint work with Graham White.

**2021-09-21 at 13:15, MVL14 and Zoom**

Tony Johansson (Chalmers)

Tony Johansson (Chalmers)

*Spanning structures in non-homogeneous random graphs*

Random graphs are often used to model real-world networks, for example the underlying social networks in some models of infectious disease outbreaks. The suitability of most models can be questioned, for two main reasons. One is clustering, absent from most random graph models, and one is degree heterogeneity, which has been addressed more in recent times by models such as the configuration model and preferential attachment models. In this talk I will discuss ways of working with non-homogeneous random graphs, focusing on the perfect matching and Hamilton cycle problems, as well as the potential of getting rid of anti-clustering conditions in some well-established proofs.

**2021-09-28 at 13:15**

Shu Shen (Sorbonne Université, Paris)

Shu Shen (Sorbonne Université, Paris)

*The Fried conjecture for admissible twists*

The relation between the spectrum of the Laplacian and the closed geodesics on a closed Riemannian manifold is one of the central themes in differential geometry. Fried conjectured that the analytic torsion, which is an alternating product of regularized determinants of the Laplacians, equals the zero value of the dynamical zeta function. In this talk, I will show the Fried conjecture on locally symmetric spaces twisted by an acyclic flat vector bundle obtained by the restriction of a representation of the underlying Lie group. This generalises the results of myself for unitarily twists, and the results of Brocker, Muller, and Wotzker on closed hyperbolic manifolds.

**2021-10-05 at 13:15**

Eusebio Gardella (MV, Chalmers/GU)

Eusebio Gardella (MV, Chalmers/GU)

*The classification problem for free ergodic actions.*

One of the basic problems in Ergodic Theory is to determine when two measure-preserving actions of a group on the atomless Borel probability space are orbit equivalent. When the group is amenable, classical results of Dye and Ornstein-Weiss show that any two such actions are orbit equivalent. Thus, the question is relevant only in the non-amenable case. In joint work with Martino Lupini, we showed that for every nonamenable countable discrete group, the relations of conjugacy and orbit equivalence of free ergodic actions are not Borel, thereby answering questions of Kechris. This means that there is in general no method, or uniform procedure, that allows us to determine when two actions of a nonamenable group are conjugate/orbit equivalent. It is a non-classification result, which rules out the existence of any classification theorems which use "nice" (Borel) invariants. The statement about conjugacy also solves the nonamenable case of Halmos' conjugacy problem in Ergodic Theory, originally posed in 1956 for ergodic transformations. The main conceptual innovation is the notion of property (T) for triples of groups, for which a cocycle superrigidity theorem à la Popa can be established. In combination with induction methods developed by Epstein, this is used to obtain a large family of free ergodic actions of the given nonamenable group which have pairwise distinct 1-cohomology groups. No previous knowledge on group amenability will be assumed, and all relevant definitions will be introduced in the course of the presentation.

**2021-10-12 at 13:15, Zoom**

Siddhartha Sahi (Rutgers Univ. N. J.)

Siddhartha Sahi (Rutgers Univ. N. J.)

*On the extension of the FKG inequality to $n$ functions*

The 1971 Fortuin-Kasteleyn-Ginibre (FKG) correlation inequality for two monotone functions on a distributive lattice is well known and has seen many applications in statistical mechanics, combinatorics, statistics, probability, and other fields of mathematics. In 2008 the speaker conjectured an extended version of this inequality for all n>2 monotone functions on a distributive lattice. This reveals an intriguing connection with the representation theory of the symmetric group. We give a proof of the conjecture for two special cases: for monotone functions on the unit square in R^k whose (upper) level sets are k-dimensional rectangles, and, more significantly, for { arbitrary} monotone functions on the unit square in R^2. The general case for R^k, k bigger than 2, remains open. This is joint work with Elliott Lieb.